# title
KRONECKER'S SOLUTION OF PELL'S EQUATION FOR CM FIELDS

# abstract
We generalize Kronecker's solution of Pell's equation to CM fields K whose Galois group over Q is an elementary abelian 2-group. This is an identity which relates CM values of a certain Hilbert modular function to products of logarithms of fundamental units. When K is imaginary quadratic, these CM values are algebraic numbers related to elliptic units in the Hilbert class field of K. Assuming Schanuel's conjecture, we show that when K has degree greater than 2 over Q these CM values are transcendental.